Question: Simplify the following expression: $n = \dfrac{-5y^2 - 50y}{40y^2 - 5y}$ You can assume $y \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-5y^2 - 50y = - (5 \cdot y \cdot y) - (2\cdot5\cdot5 \cdot y)$ The denominator can be factored: $40y^2 - 5y = (2\cdot2\cdot2\cdot5 \cdot y \cdot y) - (5 \cdot y)$ The greatest common factor of all the terms is $5y$ Factoring out $5y$ gives us: $n = \dfrac{(5y)(-y - 10)}{(5y)(8y - 1)}$ Dividing both the numerator and denominator by $5y$ gives: $n = \dfrac{-y - 10}{8y - 1}$